This paper suggests an approximation method for solving the problems of diffraction due to perfectly conducting cylinder, the section of which is a smooth curve C of arbitrary form. The principle of the method is similar to that of H. Bremmer: The field of diffraction due to a cylinder with a polygonal section (which is an inscribed polygon of the curve C) is expanded into a series. The first term of the series is the geometrical field. The second term of the series is the sum of the elementary diffraction fields due to the wedges of the polygonal cylinder. These fields are taken as those of Sommerfeld's problem, i.e., both sides of each wedge are infinitely extended. Each of these elementary fields falls on the neighbour wedge and is diffracted by the latter, and this diffracted field in turn falls on the next neighbour wedge and is again diffracted by the latter, etc. The field diffracted by the wedges one after another in such a way is called the main tangential elementary field. The third term of the series is the sum of these main tangential elementary fields. The field diffracted by wedge A, being diffracted again by the neighbour wedge B, reflects back on wedge A again, and then propagates in this direction progressively in a manner mentioned above. Such a field is called once-reflected elementary field. The fourth term of the series is the sum of these once-reflected elementary fields, etc. In general, the m-th term of the series is the sum of the (m-3) times-reflected elementary fields. Every elementary diffracted field due to any wedge is taken as the solution of Sommerfeld's problem for this wedge in the manner mentioned above. As the sides of the inscribed polygon approach to zero, the inscribed polygon approaches to the curve C, and each term of the series becomes an integral, the limit of the summation of the series approaching to the rigorous solution of the initial problem.The first three terms of the series are deduced individually. For the general m-th term a recurrent formula is given. Finally the condition of convergence of the series is discussed.